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arXiv · 1911.06885

Spectral stability of smooth solitary waves for the Degasperis-Procesi Equation

Ji Li·Yue Liu·Qiliang Wu
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Abstract

The Degasperis-Procesi equation is an approximating model of shallow-water wave propagating mainly in one direction to the Euler equations. Such a model equation is analogous to the Camassa-Holm approximation of the two-dimensional incompressible and irrotational Euler equations with the same asymptotic accuracy, and is integrable with the bi-Hamiltonian structure. In the present study, we establish existence and spectral stability results of localized smooth solitons to the Degasperis-Procesi equation on the real line. The stability proof relies essentially on refined spectral analysis of the linear operator corresponding to the second-order variational derivative of the Hamiltonian of the Degasperis-Procesi equation.

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Ji Li, Yue Liu, Qiliang Wu. 2019-11-15. Spectral stability of smooth solitary waves for the Degasperis-Procesi Equation. https://arxiv.org/abs/1911.06885

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